Description: Characterization of the elements of a class. (Contributed by BJ, 27-Jun-2019) Base on wl-dfclel.just . (Revised by Wolf Lammen, 13-Apr-2026)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | wl-dfclel | |- ( A e. B <-> E. x ( x = A /\ x e. B ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqeq1 | |- ( x = y -> ( x = A <-> y = A ) ) |
|
| 2 | eleq1w | |- ( x = y -> ( x e. B <-> y e. B ) ) |
|
| 3 | 1 2 | anbi12d | |- ( x = y -> ( ( x = A /\ x e. B ) <-> ( y = A /\ y e. B ) ) ) |
| 4 | 3 | cbvexvw | |- ( E. x ( x = A /\ x e. B ) <-> E. y ( y = A /\ y e. B ) ) |
| 5 | 4 | wl-dfclel.just | |- ( A e. B <-> E. x ( x = A /\ x e. B ) ) |